Spears was walking at a snail's pace Monday morning before heading for an MRI that revealed the injury.
Spears was injured during the Cowboys' 45-7 loss to the Green Bay Packers Sunday and it pushed starting nose tackle Jay Ratliff into double-duty. Ratliff played end and nose tackle during the game and when Josh Brent suffered cramps, Ratliff took his place as well.
Spears' injury is a major blow to a defensive line that is already missing Jason Hatcher (groin) and Sean Lissemore (ankle), who was injured Sunday.
Hatcher could miss the next two weeks and Lissemore's status hasn't been determined.
The Cowboys don't have any defensive linemen on their practice squad, and a source said the team might sign one or two to make up for the deficit.
Calvin Watkins covers the Cowboys for ESPNDallas.com.